This paper deals with Lie groupoids, in particular symplectic and contact groupoids. We formulate a deenition of contact groupoids; we give examples and a counterexample (groupoid with a contact form which is not a contact groupoid). The theory of diierentiable groupoids (called now Lie groupoids) has been introduced by C. Ehresmann E] in 1950 in his paper on connections (where he deened the gr...

In this paper we introduce the concept of ideal elements in poe-AG-groupoid and give some characterizations and properties of their ideal elements. So we consider some results concerning ideals in poe-semigroups and investigate them in poe-AG-groupoids. Also, the class of ideal elements of poe-AG-groupoids are studied, certain intrinsic and basic properties of poe-AG-groupoids including: ideal,...

We describe a part of the lattice of subvarieties of left distributive left idempotent groupoids (i.e. those satisfying the identities x(yz) ≈ (xy)(xz) and (xx)y ≈ xy) modulo the lattice of subvarieties of left distributive idempotent groupoids. A free groupoid in a subvariety of LDLI groupoids satisfying an identity x ≈ x decomposes as the direct product of its largest idempotent factor and a ...

Polynomial functors are a categorical generalization of the usual notion polynomial, which has found many applications in higher categories and type theory: those generated by polynomials consisting set monomials built from sets variables. They can be organized into cartesian bicategory, unfortunately fails to closed for essentially two reasons, we address here suitably modifying model. Firstly...

In this paper we introduced the notions of uni-soft AG-groupoids, uni-soft left(right) ideals and uni-soft quasi ideals of AG-groupoids and also investigated related properties of these structures. Some interesting Characterizations of uni-soft AG-groupoids and uni-soft left(right) ideals have been explored. Mathematics Subject Classification: 42B20, 42B25, 46E30